$k^{\phi(l)} + l^{\phi(k)} \equiv1\pmod{lk}\,$ if $\,\gcd(l,k)=1$
Solution 1:
Hint: use the Chinese Remainder Theorem (i.e. consider the experession $\pmod l$ and $\pmod k$)
Hint: use the Chinese Remainder Theorem (i.e. consider the experession $\pmod l$ and $\pmod k$)